Make four hamburger patties from ground beef, depressing the center of each patty to aid in cooking. Place in a skillet over medium heat. Pour a few drops of Worcestershire sauce over hamburger patties and sprinkle with your favorite steak seasoning. Cook until juices run clear when hamburgers are pressed with a turner.
Slice yellow onion into thin slices and place into skillet over medium heat. Drizzle with olive oil and cook until onions have turned lightly brown and are fork tender. Remove from skillet.
Lightly butter skillet or griddle over medium heat. Place one tortilla onto skillet. Cut one hamburger patty in half and place onto one side of the tortilla. Then top with a spoonful of sauce, onions, 1/4 of the lettuce, and a little of the shredded cheese. Top with another spoonful of sauce.
Fold remaining half of tortilla over filling and remove from griddle or skillet. Cut in half for serving. Serve warm.
Additional variations include: Use cooked portabello mushrooms instead of ground beef for a meatless option. Add mushrooms to your cheeseburger quesadillas for added flavor. Add a bit of jalapeno, slices of avocado and a dollop of sour cream for more of a Tex-Mex flavor for your cheeseburger quesadillas.